x² = A(x + 2)² + B(2x + 1)(x + 2) + C(2x + 1)

Let x = -2, and this gives C = -4/3.

Let x = -1/2, and this gives A = 1/9.

Comparing coefficients of x² gives: A + 2B = 1.

So B = 4/9.

Therefore

Now for the integration: